Question

Apond contains 100 fish, ofwhich 30 are carp. If 20 fish are caught, what are the mean and variance of the number of carp among the 20? What assumptions are you making?

Answer 1

Total fish = 100

Carp = 30

Number of fish caught = 20

The random variable X follows hyper-geometric distribution.

Mean = 30 *20 / 100 = 600/100 = 6

Variance = 30*20/100 * ((20-1)*(30-1)/100-1 + 1-30*20/100)

Variance = 600/100 * 56/99

Variance = 112/33

Assumptions: Is that X follows hyper-geometric distribution with the given information.